Our results also lead to several interesting counting problems.
For example, can formulae be found for the number of
elements in \(\mathcal {B}_{f,k}^r\)  or
\(\mathcal {P}_{f,k}^r\) ? In addition, using Lemma  and [1]} (see,also [2]}, [3]})
we can give a formula for the number of facets in \(\Delta (\mathcal {S}^o_{m,k})\) .
It would be interesting to see whether Theorem 
and Lemma , could be used together
with this formula to determine the number of facets in \(\Delta (\mathcal {B}^0_{f,k})\) .
